The separation or purification of physical mixtures of fine particles (called “beneficiation” in the vernacular) is accomplished primarily by establishing a bipolar charge on the constituent particle species and then using mechanical or gas conveyance to move the particles through selectively charged electrical fields. In the example of the typical arrangement shown in the schematic diagram of FIG. 1, the particles (only one oversized particle P shown for purposes of illustration) are carried by or entrained in a gaseous medium and passed through a diffuser R (including possibly with a co-flow of gas G devoid of particles) such that the direction of conveyance or flow direction F, is generally parallel to the direction of gravity (Y-axis or direction), or “vertical.” One or more electrodes (usually elongated plates, not shown) positioned adjacent to the flow create the electric field E to effect separation of particles having a selected charge (either positive or negative, depending on the charge on the electrode, but shown as having a like charge in FIG. 1) by deflecting them. In the usual arrangement, the electrode(s) are positioned such that a direction of the electric field force Fe is applied perpendicular to the flow direction F (that is, aligned with the X-axis or direction in FIG. 1, or the horizontal plane). As a result, the particle P having the selected charge is deflected in the X-direction and its trajectory T changes as it travels through this electric field “zone,” such that it may be selected out of or separated from the flow stream and collected.
Generally speaking, Newton's Laws of classical mechanics govern the motion of charged particles having diameters near or greater than atomic dimensions. Consequently, when suspended or entrained in a gas and under the influence of an electric field and gravity, the principle forces acting on a particle (assuming laminar flow, Stokes drag, no image force and Brownian motion) include:(1) gravitational force (Fg=mg);  [1.1](2) electric field force (Fe=qE);  [1.2](3) viscous force (Fx=6μπrV); and  [1.3](4) inertial force (Fi=m(dV/dt)),  [1.4]where:                E=electric field strength        μ=viscosity of medium        V=particle velocity        g=acceleration due to gravity        y=direction perpendicular to the electric field        q=charge on the particle        r=radius of the particle        m=mass of the particle        x=direction parallel to the electric fieldSumming up the forces for a vertically oriented separation system in which the gravitational force is in the Y-direction (see FIG. 2), the following is obtained:ΣFx=Fe−Fμ(x)−Fi(x)=0  [1.5]ΣFy=Fg−Fi(y)=0  [1.6]In the X-direction, the forces are:Fe−Fμ(x)−Fi(x)=0  [1.7]Substitution from Equations 1.1, 1.2, 1.3 and 1.4 into Equation 1.7 yields:        
                                          q            ⁢                                                  ⁢            E                    -                      6            ⁢                                                  ⁢            π            ⁢                                                  ⁢            r            ⁢                                                  ⁢            μ            ⁢                                                  ⁢                          V              x                                -                      m            ⁢                                          ⅆ                                  V                  x                                                            ⅆ                t                                                    =        0                            [        1.8        ]            In the Y-direction:Fg−Fi(y)=0  [1.9]Substitution yields:
                                          m            ⁢                                                  ⁢            g                    -                      m            ⁢                                          ⅆ                                  V                  y                                                            ⅆ                t                                                    =        0                            [        1.10        ]            Consequently, when oriented in the vertical orientation such that a direction of the electric field force Fe is perpendicular to the direction of gravity (Y-direction), only this force acts to deflect or move the charged particle P in the X-direction. The viscous force and inertial force actually oppose this deflection, rather than assist it.
Accordingly, a need is identified for a separation/purification systems where the forces present, including the gravitational force acting on the particles, are used to advantage, including for separating lower density particles considered impurities from higher density particles in a particle mixture.